Options are a type of derivative financial instrument, which
means they have no intrinsic value in themselves (unlike a unit of company
stock, which gives a right to a future stream of dividends), but rather derive
their value from some underlying asset. A call option gives
the holder the right to buy, at some specified time in the future, at some
specified price, an asset (in this case, a unit of stock). Correspondingly, a
put option gives the holder the right to sell such an asset at a
given date in the future.
The price of an option can be estimated using the famous BlackScholes
model, which this calculator uses. In that model, the price of the option depends
on five factors, or variables:

The price of the underlying asset

The price at which the option holder has the right to buy or sell the
underlying asset for (called the strike price)

The standard deviation of the underlying asset price (in other words, how
variable the underlying stock price is)

The interest rate on riskfree loans

The amount of time between now, and the exercise date specified by the
option (the time to expiration)
The holder of an American option has the right to buy or sell
the underlying asset at any time he/she chooses between now and the exercise
date; the holder of a European option can only exercise the
option on the exercise date itself.
In practice, the BlackScholes model is a horrendouslooking equation, and
calculating the price of an option can be a real pain, which is why a price
calculator like this can be very useful.